socceraction.atomic.vaep.formula¶

Implements the formula of the Atomic-VAEP framework.

socceraction.atomic.vaep.formula.defensive_value(actions, scores, concedes)¶

Compute the defensive value of each action.

VAEP defines the defensive value of an action as the change in conceding probability.

\[\Delta P_{concede}(a_{i}, t) = P^{k}_{concede}(S_i, t) - P^{k}_{concede}(S_{i-1}, t)\]

where \(P_{concede}(S_i, t)\) is the probability that team \(t\) which possesses the ball in state \(S_i\) will concede in the next 10 actions.

Parameters:

actions (pd.DataFrame) – SPADL action.
scores (pd.Series) – The probability of scoring from each corresponding game state.
concedes (pd.Series) – The probability of conceding from each corresponding game state.

Returns:

The defensive value of each action.

Return type:

pd.Series

socceraction.atomic.vaep.formula.offensive_value(actions, scores, concedes)¶

Compute the offensive value of each action.

VAEP defines the offensive value of an action as the change in scoring probability before and after the action.

\[\Delta P_{score}(a_{i}, t) = P^{k}_{score}(S_i, t) - P^{k}_{score}(S_{i-1}, t)\]

where \(P_{score}(S_i, t)\) is the probability that team \(t\) which possesses the ball in state \(S_i\) will score in the next 10 actions.

Parameters:

actions (pd.DataFrame) – SPADL action.
scores (pd.Series) – The probability of scoring from each corresponding game state.
concedes (pd.Series) – The probability of conceding from each corresponding game state.

Returns:

he ffensive value of each action.

Return type:

pd.Series

socceraction.atomic.vaep.formula.value(actions, Pscores, Pconcedes)¶

Compute the offensive, defensive and VAEP value of each action.

The total VAEP value of an action is the difference between that action’s offensive value and defensive value.

\[V_{VAEP}(a_i) = \Delta P_{score}(a_{i}, t) - \Delta P_{concede}(a_{i}, t)\]

Parameters:

actions (pd.DataFrame) – SPADL action.
Pscores (pd.Series) – The probability of scoring from each corresponding game state.
Pconcedes (pd.Series) – The probability of conceding from each corresponding game state.

Returns:

The ‘offensive_value’, ‘defensive_value’ and ‘vaep_value’ of each action.

Return type:

pd.DataFrame